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Comparing Quantum Gravity Models: String Theory, Loop Quantum Gravity, and Entanglement gravity versus $SU(\infty)$-QGR
General Relativity and Quantum Cosmology · Submitted 13 Sep 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We identify several common features among the studied models: importance of 2D structures; algebraic decomposition to tensor products; special role of $SU(2)$ group in their formulation; necessity of a quantum time as a relational observable.
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The abstract, sentence by sentence
In a previous work [arXiv:2009.03428] we proposed a new model for Quantum GRavity(QGR) and cosmology, dubbed $SU(\infty)$-QGR. One of the axioms of this model is that Hilbert spaces of the Universe and its subsystems represent $SU(\infty)$ symmetry group. In this framework, the classical spacetime is interpreted as being the parameter space characterizing states of the $SU(\infty)$ representing Hilbert spaces. Using quantum uncertainty relations, it is shown that the parameter space - the spacetime - has a 3+1 dimensional Lorentzian geometry. Here after a review of $SU(\infty)$-QGR, including the demonstration that its classical limit is Einstein gravity, we compare it with several QGR proposals, including: string and M-theories, loop quantum gravity and related models, and QGR proposals inspired by holographic principle and quantum entanglement. The purpose is to find their common and analogous features, even if they apparently seem to have different roles and interpretations. The hope is that such exercise gives a better understanding of gravity as a universal quantum force and clarifies the physical nature of the spacetime. We identify several common features among the studied models: importance of 2D structures; algebraic decomposition to tensor products; special role of $SU(2)$ group in their formulation; necessity of a quantum time as a relational observable. We discuss how these features can be considered as analogous in different models. We also show that they arise in $SU(\infty)$-QGR without fine-tuning, additional assumptions, or restrictions.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In a previous work [arXiv:2009.03428] we proposed a new model for Quantum GRavity(QGR) and cosmology, dubbed $SU(\infty)$-QGR. | background 0.82 | 0.43 | 0.03 | asserted 1.00 |
| s1 | One of the axioms of this model is that Hilbert spaces of the Universe and its subsystems represent $SU(\infty)$ symmetry group. | method 0.41 | 0.31 | 0.04 | asserted 1.00 |
| s2 | In this framework, the classical spacetime is interpreted as being the parameter space characterizing states of the $SU(\infty)$ representing Hilbert spaces. | interpretation 0.62 | 0.39 | 0.04 | asserted 0.99 |
| s3 | Using quantum uncertainty relations, it is shown that the parameter space - the spacetime - has a 3+1 dimensional Lorentzian geometry. | result 0.91 | 0.83 | 0.08 | asserted 1.00 |
| s4 | Here after a review of $SU(\infty)$-QGR, including the demonstration that its classical limit is Einstein gravity, we compare it with several QGR proposals, including: string and M-theories, loop quantum gravity and related models, and QGR proposals inspired by holographic principle and quantum entanglement. | contribution 0.95 | 0.72 | 0.06 | asserted 0.98 |
| s5 | The purpose is to find their common and analogous features, even if they apparently seem to have different roles and interpretations. | contribution 0.74 | 0.28 | 0.04 | asserted 0.70 |
| s6 | The hope is that such exercise gives a better understanding of gravity as a universal quantum force and clarifies the physical nature of the spacetime. | interpretation 0.61 | 0.10 | 0.05 | hedged possibility 0.73 |
| s7 | We identify several common features among the studied models: importance of 2D structures; algebraic decomposition to tensor products; special role of $SU(2)$ group in their formulation; necessity of a quantum time as a relational observable. | result 0.96 | 0.93 | 0.56 | asserted 1.00 |
| s8 | We discuss how these features can be considered as analogous in different models. | contribution 0.78 | 0.87 | 0.08 | asserted 0.74 |
| s9 | We also show that they arise in $SU(\infty)$-QGR without fine-tuning, additional assumptions, or restrictions. | result 0.94 | 0.92 | 0.31 | asserted 1.00 |
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The paper
Original abstract
In a previous work [arXiv:2009.03428] we proposed a new model for Quantum GRavity(QGR) and cosmology, dubbed $SU(\infty)$-QGR. One of the axioms of this model is that Hilbert spaces of the Universe and its subsystems represent $SU(\infty)$ symmetry group. In this framework, the classical spacetime is interpreted as being the parameter space characterizing states of the $SU(\infty)$ representing Hilbert spaces. Using quantum uncertainty relations, it is shown that the parameter space - the spacetime - has a 3+1 dimensional Lorentzian geometry. Here after a review of $SU(\infty)$-QGR, including the demonstration that its classical limit is Einstein gravity, we compare it with several QGR proposals, including: string and M-theories, loop quantum gravity and related models, and QGR proposals inspired by holographic principle and quantum entanglement. The purpose is to find their common and analogous features, even if they apparently seem to have different roles and interpretations. The hope is that such exercise gives a better understanding of gravity as a universal quantum force and clarifies the physical nature of the spacetime. We identify several common features among the studied models: importance of 2D structures; algebraic decomposition to tensor products; special role of $SU(2)$ group in their formulation; necessity of a quantum time as a relational observable. We discuss how these features can be considered as analogous in different models. We also show that they arise in $SU(\infty)$-QGR without fine-tuning, additional assumptions, or restrictions.
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How the literature uses it
5 arXiv papers cite this in 15 sentences
Papers citing it · 11 sentences without a confident label
Builds on it 1 paper
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To further advance preliminary results reported in [ref] and [ref] , in the present work we will investigate more thoroughly the structure and properties of the states of subsystems, the parameter space of representations of their $$ symmetry, and the Lagrangian of .
$SU(\infty)$ Quantum Gravity: Emergence of Gravity in an Infinitely Divisible Quantum Universe · Introduction · 0.97
Compares with it 1 paper
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is compared with both perturbative and non-perturbative approaches to string theory in [ref] .
$SU(\infty)$ Quantum Gravity: Emergence of Gravity in an Infinitely Divisible Quantum Universe · $$, Virasoro algebra and their roles in QGR · 0.94
Cites it as background 1 paper
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The importance of $SU(2) ≅SO(3)$ symmetry in QGR models is discussed in [ref] .
$SU(\infty)$ Quantum Gravity: Emergence of Gravity in an Infinitely Divisible Quantum Universe · Symmetry and Hilbert space of the Universe · 0.94
What it cites · 164 sentences without a confident label
Contests 1 paper
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The model explored in [ref] for such structures is semi-classical and includes perturbative Einstein equation, which is non-renormalizable and cannot be considered as a genuine QGR.
Gravitational splitting at first order: Quantum information localization in gravity · Comparison of LQFT-QGR with · contest 0.73
Uses the method or tool of 2 papers
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Using Mandalestam-Tam uncertainty relation [ref] , a quantity proportional to quantum fidelity of two close states $ρ$ and $ρ_1 = ρ+ dρ$ of subsystems (except reference and clock) can be defined [ref] : ds^2 ≡Q(, ρ) dt^2 = (√(dρ) √(dρ)^†), Q(ρ, ) ≡1/2 |([√(ρ), ]^2)| where $$ is a Hamiltonian operator that generates the evolution of subsystems for the selected quantum clock associated to the time parameter $t$.
Making a Quantum Universe: Symmetry and Gravity · Relation to classical geometry and Einstein equation · 0.84
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Finally, to make the above setup dynamical, a relational dynamics and evolution à la Page & Wootter [ref] or similar methods, see e.g. [ref] for a review, can be introduced by selecting one of the subsystems as a quantum clock.
The Trinity of Relational Quantum Dynamics · Parameter space of subsystems · 0.96
Cites as support 13 papers
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It confirms that Einstein equation should be considered as an equation of state [ref] and its quantization, as well as the quantization of spacetime are meaningless.
Thermodynamics of Spacetime: The Einstein Equation of State · Classical limit · 0.99
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In [ref] it is explicitly shown that, as expected, applying variational principle with respect to amplitudes $L_a$ and components of the density matrix $ρ$ leads to a vacuum state as the equilibrium solution.
Making a Quantum Universe: Symmetry and Gravity · The whole Universe · 1.00
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On the other hand, according to a corollary in a description of quantum mechanics in which symmetry is considered to be foundational [ref] , this quantum system must inevitably be decomposable to subsystem.
Symmetry as a foundational concept in Quantum Mechanics · Subsystems of the Universe · 0.98
Cites as background 25 papers
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This model is based on several axioms, see [ref] for the complete list.
Bulk Entanglement Gravity without a Boundary: Towards Finding Einstein's Equation in Hilbert Space · Entanglement-Based Models (EBM) of quantum gravity · 0.82
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According to AdS-CFT duality conjecture [ref] , and more generally gauge-gravity duality [ref] in M-theory, there is a one to one correspondence between quantum states of a suitable quantum CFT living on the boundary of a region of the spacetime and supergravity (string theory) in its AdS bulk.
Anti De Sitter Space And Holography · Anti-de Sitter - Conformal Field Theory (AdS-CFT) duality · 0.96
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According to AdS-CFT duality conjecture [ref] , and more generally gauge-gravity duality [ref] in M-theory, there is a one to one correspondence between quantum states of a suitable quantum CFT living on the boundary of a region of the spacetime and supergravity (string theory) in its AdS bulk.
The Large N Limit of Superconformal Field Theories and Supergravity · Anti-de Sitter - Conformal Field Theory (AdS-CFT) duality · 0.96
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